The fractional Landau–Lifshitz–Gilbert equation and the heat flow of harmonic maps

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• 作者：1. College of Mathematics and Statistics ; Chongqing University ; Chongqing ; 401331 People’s Republic of China2. Institute of Applied Physics and Computational Mathematics ; P.O. Box 8009 ; Beijing ; 100088 People’s Republic of China
• 关键词：35Qxx – 58E20 – 82Dxx
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2011
• 出版时间：September 2011
• 年：2011
• 卷：42
• 期：1-2
• 页码：1-19
• 全文大小：259.1 KB
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• 作者单位：http://www.springerlink.com/content/15j4137383832575/
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Systems Theory and Control
  Calculus of Variations and Optimal Control
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0835

文摘

In this paper, we prove the existence of global weak solutions to the periodic fractional Landau–Lifshitz–Gilbert equation through the Ginzburg–Landau approximation and the Galerkin approximation. Since the nonlinear term is nonlocal and of full order of the equation, some special structures of the equation, the commutator estimate and some calculus inequalities of fractional order are exploited to get the convergence of the approximating solutions. The equation considered in this paper can also be regarded as a generalization of the heat flow of harmonic maps to the fractional order.